Problem: Rewrite as a simplified fraction. ${0.9\overline{83} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 983.8383...\\ 10x &= 9.8383...\end{align*}}$ Subtracting the two equations, we have: ${990x = 974}$ ${x = \dfrac{974}{990}} $ ${x = \dfrac{487}{495}} $